Difference between revisions of "Wedge (category theory)"
From Maths
(Created page with ":: '''Note: ''' the page Cone and cocone compared redirects here as this is basically a discussion page on how the two differ (which exists because of the page Products...") |
m |
||
| Line 1: | Line 1: | ||
| − | :: '''Note: ''' the page [[Cone and cocone compared]] redirects here as this is basically a discussion page on how the two differ (which exists because of the page [[ | + | :: '''Note: ''' the page [[Cone and cocone compared]] redirects here as this is basically a discussion page on how the two differ (which exists because of the page [[Product and coproduct compared]]) |
__TOC__ | __TOC__ | ||
==Definition== | ==Definition== | ||
Latest revision as of 23:00, 28 February 2016
- Note: the page Cone and cocone compared redirects here as this is basically a discussion page on how the two differ (which exists because of the page Product and coproduct compared)
Contents
Definition
For a pair of objects [ilmath]A[/ilmath] and [ilmath]B[/ilmath] in a category [ilmath]\mathscr{C} [/ilmath] we define[1]:
| Wedge to the pair [ilmath]A[/ilmath], [ilmath]B[/ilmath] | Wedge from the pair [ilmath]A[/ilmath], [ilmath]B[/ilmath] |
|---|---|
| is an object [ilmath]X[/ilmath] in [ilmath]\mathscr{C} [/ilmath] together with a pair of arrows (also from [ilmath]\mathscr{C} [/ilmath]) as follows: | |
| [ilmath]\xymatrix{ & A \\ X \ar[ur] \ar[dr] & \\ & B}[/ilmath] | [ilmath]\xymatrix{A \ar[dr] & \\ & X \\ B \ar[ur] & }[/ilmath] |
| (AKA: cone) | (AKA: cocone) |
References
| ||||||||||||||||||||||||||||||||
